Gain-Sparsity and Symmetry-Forced Rigidity in the Plane

• Published in: Discrete & computational geometry Vol. 55; no. 2; pp. 314 - 372
• Main Authors: Jordán, Tibor, Kaszanitzky, Viktória E., Tanigawa, Shin-ichi
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.03.2016; Springer Nature B.V
• Subjects: Combinatorial analysis; Combinatorics; Computational geometry; Computational Mathematics and Numerical Analysis; Gain; Geometry; Graph theory; Graphs; Mathematics; Mathematics and Statistics; Planes; Rigidity; Symmetry; Frame matroids; Infinitesimal rigidity; Frameworks; Primary 52C25; Group-labeled graphs; Secondary 05B35; 68R10; Rigidity matroids; Symmetry; Rigidity of graphs

We consider planar bar-and-joint frameworks with discrete point group symmetry in which the joint positions are as generic as possible subject to the symmetry constraint. We provide combinatorial characterizations for symmetry-forced rigidity of such structures with rotation symmetry or dihedral sym...